Heat a grill pan over medium-high heat. Rub the steak evenly with 1 1/2 teaspoons oil; sprinkle with salt and pepper. Add the steak to the pan; cook 3 minutes on each side or until it reaches your desired degree of doneness. Remove from the pan and let stand for 5 minutes. Cut the steak across the grain into thin slices.
Cut the bread in half lengthwise and crosswise. Hollow out the tops and bottoms of the bread, leaving a 1/2 inch shell. Place the bread on a baking sheet, cut sides up. Broil 1 1/2 minutes or until toasted.
Place 1 1/2 tablespoons oil, 1/2 cup arugula, parsley, and the next 4 ingredients in a food processor. Process until finely chopped. Spread the parsley mixture evenly over the cut sides of the bread . Layer the bottom halves of the bread with the remaining arugula, steak, and tomato; cover with the top halves of bread. Cut sandwiches in half and serve!